Question 1039311
From the given that the profit p is T% of sales S, we get {{{p = (T/100)S}}}.
From the given that the profit p is P% of cost C, we get {{{p = (P/100)C}}}.

But p = S - C, so

==> {{{p = (100p)/T - (100p)/P}}}, after direct substitution.

==> {{{1 = 100/T - 100/P}}}, after dividing both sides by p.

==> {{{100/P = 100/T - 1}}}, after transposition.

==> {{{100/P = (100-T)/T}}}, after combining fractions.

==> {{{P/100 = T/(100-T)}}}, after reciprocation.

==> {{{P = (100T)/(100-T)}}}, after multiplying both sides by 100.